Methods and systems for pervasive diagnostics

ABSTRACT

Model-based production control systems and methods are presented for constructing plans for controlling operation of a production system with a plant having a plurality of resources to achieve one or more production goals, in which a planner constructs plans for execution in the plant based on production goals while balancing both production objectives (e.g., production cost, production time) and diagnostic objectives (e.g., diagnostic cost, information gained, repair cost), and a diagnosis engine determines a current plant condition based on a previously executed plan and corresponding observations from the plant, and provides expected information gain data to the planner, with the planner generating a plan that will achieve a given production goal and is improved for one or more diagnostic objectives and the expected information gain data.

BACKGROUND

The present exemplary embodiments relate to automated diagnosis andproduction in systems having multiple resources for achieving productiongoals. In such systems, automated diagnosis of system performance andcomponent status can advantageously aid in improving productivity,identifying faulty or underperforming resources, scheduling repair ormaintenance, etc. Accurate diagnostics requires information about thetrue condition of components in the production system. Such informationcan be obtained directly from sensors associated with individualcomponents and/or may be inferred from a limited number of sensorreadings within the production plant using a model or other knowledge ofthe system structure and dynamics. Providing complete sensor coveragefor all possible system faults can be expensive or impractical in harshproduction environments, and thus it is generally preferable to insteademploy diagnostic procedures to infer the source of faults detected orsuspected from limited sensors. System diagnostic information istypically gathered by one of two methods, including dedicated orexplicit diagnostics with the system being exercised while holdingproduction to perform tests and record observations without attainingany production, as well as passive diagnostics in which information isgathered from the system sensors during normal production. Although thelatter technique allows inference of some information without disruptingproduction, the regular production mode may not sufficiently exercisethe system to provide adequate diagnostic information to improve longterm productivity. Moreover, while dedicated diagnostic operationgenerally provides better information than passive diagnostics, the costof this information is high in terms of short term productivityreduction, particularly when diagnosing recurring intermittent systemcomponent failures that require repeated diagnostic interventions.Conventional production system diagnostics are thus largely unable toadequately yield useful diagnostic information without haltingproduction and incurring the associated costs of system down-time, andare therefore of limited utility in achieving long term systemproductivity. Accordingly, a need remains for improved control systemsand techniques by which both long term and short term productivity goalscan be achieved in production systems having only limited sensordeployment.

BRIEF DESCRIPTION

The present disclosure provides systems and methods for implementingon-line pervasive diagnostics in a production system, in which a plannerconstructs/generates a plan in the form of a sequence of actions takenby one or more resources in a plant based on production goals and atleast partially based on one or both of production and diagnosticobjectives or metrics. Goals, as used herein include binary conditionsthat either are or are not achieved, wherein production goals as usedherein include the production of products, modification of products,etc. Model-based production control systems and production planconstruction/generation methods are provided for controlling operationof a production system, in which a planner constructs plans forexecution in the plant based on production goals and diagnosticobjectives, and a diagnosis engine determines a current plant conditionbased on a previously executed plan and corresponding observations fromthe plant, and provides expected information gain data to the planner.Objectives as used herein constitute aspirations toward which systemsare directed, and may be achieved in whole or in part. Thus, productionobjectives may include, for example, production of products at a higherrate, or of higher quality, or more efficiently, etc., and diagnosticobjectives may include, for instance, isolating the source of systemfaults, etc.

The planner constructs a plan that will achieve a given production goalbased at least partially on a diagnostic objective and the expectedinformation gain data. In systems that do not have complete sensorcoverage, this novel approach provides significant advantages overconventional passive diagnostics in the amount of information that maybe obtained, and is significantly more cost effective in terms of shortterm productivity and may also improve long run production objectivescompared with conventional dedicated/explicit diagnostic techniques.

In accordance with one or more aspects of the present disclosure, amodel-based production control system is provided including a model, aplanner, and a diagnosis engine for controlling the operation of aproduction system that has one or more plants with resources to achieveproduction goals. The plant model includes a model of the plant and theplanner provides one or more plans for execution in the plant based onat least one output objective. The diagnosis engine determines a currentplant condition based on one or more previously executed plans, at leastone corresponding observation from the plant, and the plant model. Thediagnosis engine also provides expected information gain data to theplanner for one or more possible plans based on the current plantcondition and the model. The planner generates or constructs a plan thatwill achieve a given production goal at least partially based on adiagnostic objective and the expected information gain data. Thiscontrol system facilitates the inclusion of diagnostic objectives andexpected diagnostic information gain into the generation of productionplans, and thus may be implemented to provide more useful diagnosticinformation than conventional passive diagnostic techniques, while stillavoiding or mitigating system down-time.

The control system is flexible in allowing the planner to also constructor generate dedicated diagnostic plans based on one or more particulardiagnostic objectives and the current plant condition, where theinformation to be gained may substantially improve the ability torealize long term productivity improvements. The planner may selectivelyinterleave dedicated diagnostic plans and production plans for executionin the plant based on at least one production goal and at least onediagnostic objective. The diagnostic objective may be updated based atleast partially on the expected information gain data. The controlsystem may also include an operator interface that allows an operator toprovide observations that the diagnosis engine can use in determiningthe current plant condition and a diagnosis job description languageallowing definition of a diagnostic plan. In addition the current plantcondition and the plant model may be used at least partially by theplanner to generate/construct a control plan or a sequence of controlplans for the plant that will achieve a set of production goals whilebalancing both production objectives (e.g., production cost, productiontime) and diagnostic objectives (e.g., diagnostic cost, informationgained, repair cost) to perform diagnosis in isolating faulty resourcesin the plant.

Further aspects of the disclosure relate to a method of constructing orgenerating plans for execution in a production system with a planthaving a plurality of resources to achieve one or more production goals.In this method, a current plant condition is determined based at leastpartially on a previously executed plan, at least one correspondingobservation from the plant, and a plant model. The method also includesdetermining expected information gain data for one or more possibleplans based on the current plant condition and the model, andconstructing a plan that will achieve a given production goal based atleast partially on a diagnostic objective and the expected informationgain data. The plan construction may also be based on the current plantcondition, and may include making a tradeoff between productionobjectives and diagnostic objectives and/or may further includeperforming diagnosis to isolate faulty resources in the plant at leastpartially based on the current plant condition. The method may furtherinclude constructing a dedicated or explicit diagnostic plan as well asselectively interleaving dedicated diagnostic plans and production plansbased on at least one production goal and at least one diagnosticobjective. In addition, the method may include allowing a user to definea diagnostic plan using a diagnosis job description language, as well asreceiving user observations and constructing the plan at least partiallybased on the user observations.

In accordance with still other aspects of the disclosure, a computerreadable medium is provided, which has computer executable instructionsfor performing the steps of determining a current plant condition basedat least partially on a previously executed plan, at least onecorresponding observation from the plant, and a plant model, anddetermining expected information gain data for one or more possibleplans based on the current plant condition and the model. Computerexecutable instructions are also provided for constructing a plan forexecution in the plant that will achieve a given production goal basedat least partially on a diagnostic objective and the expectedinformation gain data. The computer readable medium may also includecomputer executable instructions for constructing the plan based atleast partially on the current plant condition.

BRIEF DESCRIPTION OF THE DRAWINGS

The present subject matter may take form in various components andarrangements of components, and in various steps and arrangements ofsteps. The drawings are only for purposes of illustrating preferredembodiments and are not to be construed as limiting the subject matter.

FIG. 1 is a schematic diagram illustrating a production system and anexemplary model-based control system with a planner, a plant model, adiagnosis engine, and a operator interface in accordance with one ormore aspects of the disclosure;

FIG. 2 is a schematic diagram illustrating further details of anexemplary modular printing system plant in the production system of FIG.1;

FIG. 3 is a schematic diagram illustrating further details of theexemplary planner and diagnosis engine in the control system of FIGS. 1and 2;

FIG. 4 is a schematic diagram illustrating a plan space for a productionsystem, including production and diagnostic plans;

FIG. 5 is a flow diagram illustrating an exemplary method forconstructing plans for execution in a production system in accordancewith one or more aspects of the present disclosure;

FIG. 6 is a flow diagram illustrating an exemplary method of evaluatingand generating plans for execution in the plant using an A* search;

FIG. 7 is a schematic diagram illustrating an exemplary state/actiondiagram showing possible plans for transitioning the system state from astarting state to a goal state;

FIGS. 8-16 are graphs showing simulated cost vs. time curves forpassive, explicit, and pervasive diagnosis techniques in the system ofFIGS. 1-3; and

FIG. 17 is a schematic flow diagram illustrating construction of plansin the system of FIGS. 1-3 using a SAT solver in accordance with furtheraspects of the disclosure.

DETAILED DESCRIPTION

Referring now to the drawing figures, several embodiments orimplementations of the present disclosure are hereinafter described inconjunction with the drawings, wherein like reference numerals are usedto refer to like elements throughout, and wherein the various features,structures, and graphical renderings are not necessarily drawn to scale.The disclosure relates to production systems generally and ishereinafter illustrated and described in the context of exemplarydocument processing systems having various printing and documenttransport resources. However, the concepts of the disclosure also findutility in association with product packaging systems and any other typeor form of system in which a plurality of resources, whether machines,humans, software or logic components, objects, etc., may be selectivelyemployed according to plans comprised of a series of actions to achieveone or more production goals based at least partially on one or morediagnostic metrics or objectives, wherein all such alternative orvariant implementations are contemplated as falling within the scope ofthe present disclosure and the appended claims. The disclosure findsparticular utility in constructing and scheduling plans in systems inwhich a given production goal can be achieved in two or more differentways, including use of different resources (e.g., two or more printengines that can each perform a given desired printing action, twodifferent substrate routing paths that can be employed to transport agiven printed substrate from one system location to another, etc.),and/or the operation of a given system resource at different operatingparameter values (e.g., operating substrate feeding components atdifferent speeds, operating print engines at different voltages,temperatures, speeds, etc.).

FIGS. 1-3 illustrate on such system 1 in which the various aspects ofthe present disclosure may be implemented. As best shown in FIG. 1, aproduction system 6 is illustrated including a producer component 10that receives production jobs 49 from a customer 4 and a plant 20 havinga plurality of resources 21-24 that may be actuated or operatedaccording to one or more plans 54 so as to produce one or more products52 for provision to the customer 4 by the producer 10, where ‘producing’products can include modifying products, objects, etc., includingwithout limitation packaging or wrapping products. FIG. 2 illustratesfurther details of one exemplary plant 20 and FIG. 3 shows additionaldetails regarding the exemplary model-based control system 2. Theproducer 10 manages one or more plants 20 which actually produce theoutput products 52 to satisfy customer jobs 49. The producer 10 in thisembodiment provides jobs and objectives 51 to a multi-objective planner30 of the model-based control system 2 and the production system 6receives plans 54 from the planner 30 for execution in the plant 20. Thejobs 54 can include one or both of production and diagnostic goals. Asshown in FIG. 1, the control system 2 further includes a plant model 50with a model of the plant 20, and a diagnosis engine 40 with a beliefmodel 42. The diagnosis engine 40 determines and updates a current plantcondition 58 via a plant condition estimation/updating component 44(FIG. 3) based on one or more previously executed plans 54,corresponding observations 56 from the plant 20, and the model 50. Thediagnosis engine 40 also provides expected information gain data 70 tothe planner 30 for one or more possible plans 54 based on the currentplant condition 58 and the model 50.

The model-based control system 2 and the components thereof may beimplemented as hardware, software, firmware, programmable logic, orcombinations thereof, and may be implemented in unitary or distributedfashion. In one possible implementation, the planner 30, the diagnosisengine 40, and the model 50 are software components and may beimplemented as a set of sub-components or objects including computerexecutable instructions and computer readable data executing on one ormore hardware platforms such as one or more computers including one ormore processors, data stores, memory, etc. The components 30, 40, and 50and sub components thereof may be executed on the same computer or indistributed fashion in two or more processing components that areoperatively coupled with one another to provide the functionality andoperation described herein. Likewise, the producer 10 may be implementedin any suitable hardware, software, firmware, logic, or combinationsthereof, in a single system component or in distributed fashion inmultiple interoperable components. In this regard, the control system 2may be implemented using modular software components (e.g., model 50,planner 30, diagnosis engine 40 and/or sub-components thereof) tofacilitate ease of debugging and testing, the ability to plug state ofthe art modules into any role, and distribution of operation overmultiple servers, computers, hardware components, etc.

The embodiment of FIG. 1 also includes an optional operator interface 8implemented in the computer or other platform(s) on which the othercomponents of the control system 2 are implemented, although not astrict requirement of the disclosure, wherein the operator interface 8may alternatively be a separate system operatively coupled with thecontrol system 2. The exemplary operator interface 8 is operativelycoupled with the diagnosis engine 40 to provide operator observations 56a to the diagnosis engine 40, with the diagnosis engine 40 determiningthe current plant condition 58 based at least partially on the operatorobservations 56 a in certain implementations. Moreover, the exemplaryoperator interface 8 allows the operator to define a diagnostic job 8 busing a diagnosis job description language 8 a, and the diagnosis engine40 may provide diagnostic jobs 60 to the producer 10. The diagnosisengine 40 in this implementation is operative to selectively provide oneor more self-generated diagnostic jobs 60 and/or operator defineddiagnostic jobs 8 b to the producer 10, which in turn provides jobs andobjectives 51 to the planner 30.

Referring also to FIGS. 2 and 3, the planner 30 provides one or moreplans 54 to the production system 6 for execution in the plant 20 basedon at least one output objective 34 (FIG. 3) and production goals asdirected by the incoming jobs 51 from the producer 10. As shown in FIG.3, the planner 30 selectively factors in one or more output objectives34 derived from the jobs and objectives 51 in constructing plans 54including production objectives 34 a and diagnostic objectives 34 b. Inone possible implementation, the production objectives 34 a are createdand updated according to the jobs and objectives 51 obtained from theproduction system 6, and the diagnostic objectives 34 b are derived fromand updated according to the current plant condition 58 and the expectedinformation gain data 70 provided by the diagnosis engine 40. Theproduction objectives 34 a in one implementation may relate to thescheduling of orders for produced products 52 (FIG. 1), and may includeprioritization of production, minimization of inventory, and otherconsiderations and constraints driven in large part by cost and customerneeds. Examples of production objectives 34 a include prioritizing planconstruction/generation with respect to achieving a given product outputgoal (simple production criteria) as well as a secondary considerationsuch as simple time efficient production, cost efficient production, androbust production. For instance, cost efficient production objectives 34a will lead to construction/generation of plans 54 that are the mostcost efficient among the plans that met the production goal as dictatedby the jobs 51 received from the producer 10. The diagnostic objectives34 b may include objectives related to determining preferred actionsequences in generated plans 54 for performing a givenproduction-related task, minimization of maintenance and repair costs inoperation of the plant 20, identifying resources 21-24 causingintermittent or persistent faults, etc.

As further shown in FIG. 3, the control system 2 may optionally includea plan data store or database 36 used to store plans 54 selectable bythe planner 30 for execution in the plant 20 to facilitate one or moreproduction or diagnostic objectives 34, wherein construction/generationof a plan 54 as used herein can include selection of one or morepre-stored plans 54 from the data store 36. In this regard, the planner30 can selectively re-order a job queue so as to improve the likelihoodof information gain. Although illustrated as integral to the planner 30,the plan data store 36 may be provided in a separate component orcomponents that are operatively coupled with the planner 30 by which theplanner 30 can obtain one or more plans 54 (whole and/or partial)therefrom. Alternatively or in combination, the planner 30 cansynthesize (e.g. construct or generate) one or more plans 54 as needed,using the plant model 50 and information from the producer 10 anddiagnosis engine 40 to determine the states and actions required tofacilitate a given production and/or diagnostic objectives 34.

The planner 30 creates and provides plans 54 for execution in the plant20. The plans 54 include a series of actions to facilitate one or moreproduction and/or diagnostic objectives 34 while achieving a productiongoal according to the jobs 51, and in which a given action may appearmore than once. The actions are taken with respect to states andresources 21-24 defined in the model 50 of the plant 20, for example, toroute a given substrate through a modular printing system 20 from astarting state to a finished state as shown in FIG. 2. In operation, theplanner 30 generates or constructs a plan 54 that will achieve a givenproduction goal at least partially based on a diagnostic objective 34 band the expected information gain data 70 from the diagnosis engine 40.The planner 30 in the illustrated embodiment includes a goal-based planconstruction component 32 that assesses the current plant condition 58from the diagnosis engine 40 in generating a plan 54 for execution inthe plant 20. The component 32 may also facilitate identification offaulty components 21-24 or sets thereof in constructing the plans 54based on observations 56 and current plant conditions 58 indicating oneor more plant components 21-24 as being suspected of causing systemfaults.

Referring also to FIG. 4, the presently disclosed intelligent planconstruction techniques advantageously provide for generation of plans54 for execution in the plant 20 within a plan space 100 that includesboth production plans 102 and diagnostic plans 104. As seen in thediagram of FIG. 4, the union of the plan sets 102 and 104 includesproduction plans 106 that have diagnostic value (e.g., can facilitateone or more diagnostic objectives 34 b in FIG. 3), wherein the planner30 advantageously utilizes information from the diagnosis engine 40 topreferentially construct plans 106 that achieve production goals whileobtaining useful diagnostic information in accordance with thediagnostic objectives 34 b. The intelligent plan construction aspects ofthe present disclosure thus integrate the production planning anddiagnosis to facilitate the acquisition of more useful diagnosticinformation compared with conventional passive diagnostic techniqueswithout the down-time costs associated with conventional dedicateddiagnostics. The diagnostic information gained, in turn, can be used toimprove the long term productivity of the system 6, thereby alsofacilitating one or more production objectives 34 a (FIG. 3).

As further illustrated in FIG. 3, the diagnosis engine 40 in oneembodiment includes a belief model 42 representing the current state ofthe plant 20, and a component 44 that provides the current condition ofthe plant 20 to the planner 30 based on the previous plan(s) 54 andcorresponding plant observations 56. The component 44 also estimates andupdates the plant condition of the belief model 42 according to theplant observations 56, the plant model 50, and the previously executedplans 54. The operator observations 56 a from the interface 8 may alsobe used to supplement the estimation and updating of the current plantcondition by the component 44. The estimation/updating component 44provides the condition information 58 to inform the planner 30 of theconfirmed or suspected condition of one or more resources 21-24 or othercomponents of the plant 20 (FIG. 1). This condition information 58 maybe considered by the plan construction component 32, together withinformation about the plant 20 from the plant model 50 in providingplans 54 for implementing a given production job or goal 51, inconsideration of production objectives 34 a and diagnostic objectives 34b. The diagnosis engine 40 also includes a component 46 that providesexpected information gain data 70 to the planner 30 based on the model50 and the belief model 42. The information gain data 70 may optionallybe determined in consideration of the operator defined diagnostic jobs 8b from the operator interface 8.

FIG. 2 illustrates further details of an exemplary modular printingsystem plant 20 in the production system 6, including material supplycomponent 21 that provides printable sheet substrates from one of twosupply sources 21 a and 21 b, a plurality of print or marking engines22, an output finisher station 23, a modular substrate transport systemincluding a plurality of bidirectional substrate transport/routercomponents 24 (depicted in dashed circles in FIG. 2), one or more outputsensors 26 disposed between the transport system 24 and the finisher 23,and a controller 28 providing control signals for operating the variousactuator resources 21-24 of the plant 20. The exemplary printing systemplant 20 includes four print engines 22 a, 22 b, 22 c, and 22 d,although any number of such marking engines may be included, and furtherprovides a multi-path transport highway with three bidirectionalsubstrate transport paths 25 a, 25 b, and 25 c, with the transportcomponents 24 being operable by suitable routing signals from thecontroller 28 to transport individual substrate sheets from the supply21 through one or more of the marking engines 22 (with or withoutinversion for duplex two-side printing), and ultimately to the outputfinishing station 23 where given print jobs are provided as outputproducts 52. Each of the printing engines 22, moreover, may individuallyprovide for local duplex routing and media inversion, and may be singlecolor or multi-color printing engines operable via signals from thecontroller 28. The model-based control system 2 may, in certainembodiments, be integrated into the plant controller 28, although not astrict requirement of the present disclosure.

Referring now to FIGS. 1-3, in operation, the planner 30 automaticallygenerates plans 54, for example, by piece-wise determination of a seriesof actions to form a plan and/or by obtaining whole or partial plans 54from the data store 36 for component resources 21-24 of the printingsystem plant 20 from a description of output production goals derivedfrom the incoming jobs 51 in consideration of one or more productionobjectives 34 a and diagnostic objectives 34 b. In particular, when theplant 20 has flexibility in how the output goals can be achieved (e.g.in how the desired products 52 can be created, modified, packaged,wrapped, etc.), such as when two or more possible plans 54 can be usedto produce the desired products 52, the diagnosis engine 40 can alter orinfluence the plan construction operation of the planner 30 to generatea plan 54 that is expected to yield the most informative observations56. The constructed plan 54 in this respect may or may not result in aplan that compromises short term production objectives 34 a (e.g.,increases job time or slightly lowers quality), but productionnevertheless need not be halted in order for the system to learn. Theadditional information gained from execution of the constructed job 54can be used by the producer 10 and/or by the planner 30 and diagnosisengine 40 to work around faulty component resources 21-24, to scheduleeffective repair/maintenance, and/or to further diagnose the systemstate (e.g., to confirm or rule out certain system resources 21-24 asthe source of faults previously detected by the sensor(s) 26). In thismanner, the information gleaned from the constructed plans 54 (e.g.,plant observations 56) can be used by the estimation and updatingcomponent 44 to further refine the accuracy of the current belief model42.

Moreover, where the plant 20 includes only limited sensing capabilities,(e.g., such as the system in FIG. 2 having only sensors 26 at the outputof the transport system 24 downstream of the printing engines 22),passive diagnosis are unable to unambiguously identify every possiblefault in the system 20, whereas direct diagnostic efforts lead to systemdown-time and the associated cost in terms of productivity. The controlsystem 2 of the present disclosure, on the other hand, advantageouslyfacilitates selective employment of intelligent on-line diagnosis thoughconstruction and execution of plans 54 that provide enhanced diagnosticinformation according to the plant condition 58 and/or the expectedinformation gain 70, and may further advantageously facilitategeneration of one or more dedicated diagnostic plans 54 for execution inthe plant 20 based on at least one diagnostic objective 34 b and theplant condition 58, and for intelligent interleaving of dedicateddiagnostic plans 54 and production plans 54 based on production anddiagnostic objectives 34 according to the current plant condition 58. Inparticular, the planner 30 can cause execution of explicit diagnosticplans 54 that involve halting production when the information gainedfrom the plan 70 is expected to lead to significant future gains inproductivity, enhanced ability to identify faulty resources 21-24, orother long term productivity objectives 34 a and/or diagnosticobjectives 34 b.

Even without utilizing dedicated diagnostic plans 54, moreover, thecontrol system 6 significantly expands the range of diagnosis that canbe done online through pervasive diagnostic aspects of this disclosureduring production (e.g., above and beyond the purely passive diagnosticcapabilities of the system), thereby lowering the overall cost ofdiagnostic information by mitigating down time, the number of servicevisits, and the cost of unnecessarily replacing components 21-24 in thesystem 20 that are actually working, without requiring complete sensorcoverage. The planner 30 is further operative to use the current plantcondition 58 in making a tradeoff between production objectives 34 a anddiagnostic objectives 34 b in generating plans 54 for execution in theplant 20, and may also take the condition 58 into account in performingdiagnosis in isolating faulty resources 21-24 in the plant 20.

The plant condition estimation and updating component 44 of thediagnosis engine 40 infers the condition of internal components 21-24 ofthe plant 20 at least partially from information in the form orobservations 56 derived from the limited sensors 26, wherein thediagnosis engine 40 constructs the plant condition 58 in one embodimentto indicate both the condition (e.g., normal, worn, broken) and thecurrent operational state (e.g., on, off, occupied, empty, etc.) of theindividual resources 21-24 or components of the plant 20, and the beliefmodel 42 can be updated accordingly to indicate confidence in theconditions and/or states of the resources or components 21-24. Inoperation of the illustrated embodiment, once the producer 10 hasinitiated production of one or more plans 54, the diagnosis engine 40receives a copy of the executed plan(s) 54 and correspondingobservations 56 (along with any operator-entered observations 56 a). Thecondition estimation and updating component 44 uses the observations 56,56 a together with the plant model 50 to infer or estimate the condition58 of internal components/resources 21-24 and updates the belief model42 accordingly. The inferred plant condition information 58 is used bythe planner 30 to directly improve the productivity of the system 20,such as by selectively constructing plans 54 that avoid using one ormore resources/components 21-24 known (or believed with highprobability) to be faulty, and/or the producer 10 may utilize thecondition information 58 in scheduling jobs 51 to accomplish suchavoidance of faulty resources 21-24. The exemplary diagnosis engine 40also provides future prognostic information to update the diagnosticobjectives 34 b which may be used by the planner 30 to spreadutilization load over multiple redundant components 21-24 to create evenwear or to facilitate other long term objectives 34.

To improve future productivity, moreover, the diagnosis engine 40provides the data 70 to the planner 30 regarding the expectedinformation gain of various possible production plans 54. The planner30, in turn, can use this data 70 to construct production plans 54 thatare maximally diagnostic (e.g., most likely to yield information ofhighest diagnostic value). In this manner, the planner 30 can implementactive diagnostics or active monitoring by using carefully generated ormodified production plans 54 to increase information during production(e.g., using ‘diagnostic’ production plans). Moreover, certaindiagnostic plans 54 are non-productive with respect to the plant 20, butnevertheless may yield important diagnostic information (e.g., operatingthe transport mechanisms 24 in FIG. 2 such that all the substratetransport paths 25 a, 25 b, and 25 c go in the backward direction awayfrom the output finisher 23). Within this space of plans 54 that do notaccomplish any production goals, the operator interface 8 allows anoperator to create diagnostic jobs 8 b via the job description language8 a, and the diagnosis engine 40 may also include a diagnosis jobdescription language to generate dedicated/explicit diagnostic jobs 60which are provided to the producer 10. The producer 10 may then providethese jobs 60 to the planner 30 along with the other jobs and objectives51 to explicitly request the planner 30 to advance diagnostic objectives34 b. The producer 10 in one implementation may operate a job queue thatqueues requested customer and diagnostic jobs 49, 60 and the producer 10receives component condition updates 58 from the diagnosis engine 40.The producer 10 uses the condition 58 to choose between customer jobs 49and diagnosis jobs 60, to tradeoff production efficiency versusdiagnostic value in production plans 54, and to merge (e.g., interleave)customer jobs 49 and dedicated diagnostic jobs 60 when they arecompatible and wherein the scheduling thereof can facilitate one or morediagnostic and production objectives 34. The diagnosis engine 40 canalso provide prognostic information to the planner 30 to help improvethe quality of the plans 54 with respect to certain criteria. Forexample, the planner 30 (e.g., and/or the producer 10) is operative toselectively use fault state information to construct from multiplesuitable production plans 54 based on the prognosis of plan alternativesfor “robust printing” to distribute workload evenly across differentresources 21-24 in order to reduce the frequency of scheduled orunscheduled maintenance of the plant 20.

Referring also to FIG. 5, an exemplary method 200 is illustrated forconstructing plans 54 for execution in a production system 6 with aplant 20 having a plurality of resources 21-24 to achieve one or moreproduction goals. While the method 200 is illustrated and describedbelow in the form of a series of acts or events, it will be appreciatedthat the various methods of the disclosure are not limited by theillustrated ordering of such acts or events. In this regard, except asspecifically provided hereinafter, some acts or events may occur indifferent order and/or concurrently with other acts or events apart fromthose illustrated and described herein in accordance with thedisclosure. It is further noted that not all illustrated steps may berequired to implement a process or method in accordance with the presentdisclosure, and one or more such acts may be combined. The illustratedmethod 200 other methods of the disclosure may be implemented inhardware, software, or combinations thereof, such as in the exemplarycontrol system 2 described above, and may be embodied in the form ofcomputer executable instructions stored in a computer readable medium,such as in a memory operatively associated with the control system 2 inone example.

Diagnostic objectives 34 b are received at 202 in the method 200. Themethod 200 further includes determining a current plant condition 58 at204 based at least partially on a previously executed plan 54 and atleast one corresponding observation 56 from the plant 20 using a plantmodel 50, and determining expected information gain data 70 at 206 basedon the current plant condition 58 and the model 50. The planner 30receives the plant conditions 58 at 208 from the diagnosis engine 40,and receives production jobs and objectives 51 at 210 from the producer10. At 212, the planner 30 constructs a plan 54 at based at leastpartially on a diagnostic objective 34 b and the expected informationgain data 70. At 214, the planner 30 sends the constructed plan 54 tothe plant 20 for execution and the diagnosis engine 40 receives the plan54 and the plant observations 56 at 216. At 218, the diagnosis engine 40updates the plant condition 58 and updates the expected information gaindata 70, after which further jobs and objectives 51 are serviced and theprocess 200 continues again at 210 as described above.

The plan construction at 212 may be based at least partially on thecurrent plant condition 58, and may include making a tradeoff betweenproduction objectives 34 a and diagnostic objectives 34 b based at leastpartially on the current plant condition 58. Moreover, the planconstruction at 212 may include performing prognosis to isolate faultyresources 21-24 in the plant 20 based at least partially on the currentplant condition 58. In certain embodiments, a dedicated diagnostic plan54 may be constructed for execution in the plant 20 based at leastpartially on at least one diagnostic objective 34 b, a diagnostic job60, 8 b, and the current plant condition 58, and the plan constructionmay provide for selectively interleaving dedicated diagnostic andproduction plans 54 based on at least one production objective 34 a andat least one diagnostic objective 34 b. Further embodiments of themethod 200 may also include allowing an operator to define a diagnosticplan 8 b using a diagnosis job description language 8 a and receivingoperator observations 56 a, with the plan selection/generation at 216being based at least partially on the operator observations 56 a.

In accordance with further aspects of the present disclosure, a computerreadable medium is provided, which has computer executable instructionsfor performing the steps of determining a current plant condition 58 ina production system 6 with a plant 20 having a plurality of resources21-24 based at least partially on a previously executed plan 54, atleast one corresponding observation 56 from the plant 20, and a plantmodel 50, and computer executable instructions for determining expectedinformation gain data 70 based on the current plant condition 58 and themodel 50. The medium further includes instructions for constructing aplan 54 for execution in the plant 20 to achieve one or more productiongoals based at least partially on a diagnostic objective 34 b and theexpected information gain data 70. In various embodiments, furthercomputer executable instructions are included in the medium forconstructing the plan 54 based at least partially on the current plantcondition 58.

Referring now to FIGS. 6 and 7, a variety of techniques can be employedby the planner 30 in the above described control system 6 inconstructing plans 54 to enhance diagnostic information gain whileachieving production goals. In one embodiment, a heuristic search isemployed by the planner 30 in constructing diagnostic production plans54. FIG. 6 illustrates an exemplary method 300 for evaluating andconstructing plans for execution in the plant 20 using A* search. Inthis embodiment, the component 44 of the diagnosis engine 40 (FIG. 3)establishes and updates beliefs in the belief model 42 about the plantconditions and updates the plant model 50. At 302 in FIG. 6, thecomponent 44 derives failure or fault probabilities for each faulthypothesis in the plant 20 and employs dynamic programming at 304 togenerate a upper and lower plan failure probability bounding heuristicbased on the belief model 42 and the current plant condition 58. At 306,the planner 30 uses the heuristic to evaluate partial plans 54 so as toconstruct maximally informative plans 54, preferably using an A* searchapproach. At 308, the diagnosis engine 40 then uses the constructed plan54 and output observations 56 obtained from execution of the constructedplan 54 in the plant 20 to update the belief model 42.

The diagnosis engine 40 in this approach advantageously provides theinputs for searching by the planner 30 in order to derive valuableinformation for the diagnosis of the system 20. In this embodiment, thebest plans 54 with respect to diagnostic value for single persistentfaults are those that have an equal probability of succeeding orfailing. The diagnosis engine 40 uses this notion to develop heuristicsto guide the search by the planner 30 in evaluating partial plans 54 toconstruct the plan 54 to be executed in the plant 20. In addition, theplan construction search may employ pruning techniques to improve searchperformance. By this approach, the control system 2 implements efficienton-line active or pervasive diagnosis in controlling the plant 20through a combination of model-based probabilistic inference in thediagnosis engine 40 with decomposition of the information gainassociated with executing a given plan 54 using an efficient heuristictarget search in the planner 30. In this active diagnosis technique,specific inputs or control actions in the form of plans 54 areconstructed by the planner 30 with the help of the diagnosis engine 40to maximize or increase the amount and/or quality of diagnosticinformation obtained from the controlled system plant 20. Theinformative production (active or pervasive diagnosis) techniques of thepresent disclosure rank the set of partial plans at any given point inthe construction process that achieve production goals by theirpotential information gain and the planner 30 operates to selectivelygenerate the most promising strategy in that respect, in considerationof other possible production objectives 34 a and diagnosis objectives 34b.

As discussed above in the context of the exemplary modular printingsystem plant 20 of FIG. 2, the planner 30 operates to construct thesequence of actions (plan 54) that transfers substrate sheets throughthe system 20 to generate a requested output for a given print job (e.g.to satisfy a production goal), using pervasive diagnosis to aid in planconstruction. One particular production objective 34 a in this system 20is to continue printing even if some of the print engines 22 fail orsome of the paper handling modules 24 fail or jam. In this exemplarymodular printing system example 20, moreover, there are only output typesensors 26 preceding the finisher 23, and as a result, a plan 54consisting of numerous actions must be executed before a usefulobservation 56 can be made. The diagnostic engine 40 updates its beliefmodel 42 and the current condition 58 to be consistent with the executedplan 54 and the observations 56. The diagnosis engine 40 forwardsupdated condition information 58 and the expected information gain data70 to the planner 30.

In the exemplary planner 30, a search algorithm may be employed to findand construct plans 54. The model 50 describes the plant system 20 as astate machine with all possible actions A that the plant 20 canaccommodate. Actions are defined by preconditions and post-conditionsover the system state. As such, an action requires the system 20 to bein a certain state in order to be executable and modifies the systemstate when executed. The system 20 is controlled by plan p (54) that iscomprised of a sequence of actions a₁, a₂, . . . , a_(n) drawn from theset A of possible actions. Execution of an action potentially changesthe system state, and part of the system state may represent the stateof a product 52 at any given time, particularly if the action is part ofa production plan 54. Further, internal constraints of the system 54limit the set of plans 54 to a subset of all possible sequences (e.g.,the plan space 100 in FIG. 4 above). Moreover, the execution of actionsof a given plan p in the system 20 may result in only a singleobservable plan outcome or observation O (e.g., observation 56 fromsensor 26).

One type of observable outcome 26 is defined as abnormal, denoted ab(p),in which the plan 54 fails to achieve its production goal. Another typeis a normal (not abnormal) outcome, denoted

ab(p) in which the plan 54 achieves the associated production goal. Inthe exemplary control system 2, information about the plant 20 may berepresented by the diagnosis engine's belief in various possiblehypotheses, constituted in the belief model 42, where such a hypothesish is an assignment of abnormal or normal to each of the system actionse.g., h=[ab(a₁),

ab(a₂), . . . , ab(a_(n))]. In the example case of a fault in a singleplant resource/component (single fault case), exactly one action will beabnormal. Defining H_(SYS) as a set of all hypotheses excluding a singlehypothesis (a “no fault” hypothesis h₀) for the situation where allactions are normal, every hypothesis is a complete assignment ofabnormality to each action, and all are unique and mutually exclusive(e.g., ∀h_(i), h_(j)∈H_(sys), h_(i)≠h_(j)). The system's beliefs in thebelief model 42 can be represented as a probability distribution overthe hypothesis space H_(sys), Pr(H), where the belief model 42 isupdated by the diagnosis engine 40 from past observations 56 usingBayes' rule to get a posterior distribution over the unknown hypothesisH given observation O and plan P: Pr(H|O, P)=αPr(O|H, P)Pr(H).

A plan p is deemed by the diagnosis engine 40 and the planner 30 asbeing informative if it contributes information to (e.g., reduces theuncertainty of) the diagnosis engine's beliefs 42, where the informativevalue can be measured as the mutual information between the systembeliefs Pr(H) and the plan outcome conditioned on the plan executed,I(H; O|P=p). This mutual information may be defined in terms of entropyor uncertainty implied by a probability distribution, where a uniformprobability distribution has high uncertainty and a deterministicdistribution has low uncertainty. In the context of diagnosticinformation value, an informative plan 54 reduces the uncertainty of thesystem's beliefs 42, and thus plans 54 with outcomes that are hard topredict are the most informative, while execution of plans 54 that areknown to succeed (or known to fail) will yield no diagnostic informationgain. In this respect, an optimal (e.g., ‘target’) uncertainty T may beused to rate the plans 54 with respect to expected informative value, bywhich the diagnosis engine 40 can evaluate plans 54 accordingly andprovide the expected information gain data 70 to the planner 30 toinfluence the plan selection/generation for preferentialselection/generation of informative plans 54.

In the case of persistent single faults, a value of T=0.5 can be use asthe optimal uncertainty about the outcome, and uncertainty in the caseof intermittent faults may be maximized in the range of about 0.36≦T≦0.5in one exemplary implementation. In finding a plan 54 with a givenamount of uncertainty T, the diagnosis engine 40 is operative to predictthe uncertainty associated with a given plan p=[a₁, a₂, . . . , a_(n)],where the set of unique actions in a plan A_(p)=U_(i) {a_(i)∈p}.Presuming f failures are observable, a plan 54 will be abnormal ab(p) ifone or more of its actions are abnormal, as set forth in the followingequation (1):ab(a₁)ν . . . νab(a_(n))

ab(p) for a_(i)∈A_(p)  (1)where a_(i) ∈A_(p), and p is the plan. The predicted probability of anaction of a plan 54 being abnormal will be a function of the probabilityassigned to all relevant hypotheses, where the set of hypotheses thatinfluence the uncertainty of the outcome of plan p is denoted H_(p) andis defined in the following equation (2):H _(p) ={h|h∈H _(sys) and h

ab(a), a∈A _(p)}.  (2)

Given a distribution over hypotheses and the set Hp of explanatoryhypotheses for a given plan p, it is possible to calculate theprobability that plan p will fail. Since every hypothesis h∈H_(p)contains at least one abnormal action that is also in plan p, hypothesish being true implies ab(p):(h₁νh₂ν . . . νh_(m))

ab(p) where h_(j)∈H_(p)  (3)

Since the hypotheses are mutually exclusive by definition, theprobability of a plan failure Pr(ab(p)) can be defined as the sum of allprobabilities of hypotheses which imply that the plan will fail, as inthe following equation (4):

$\begin{matrix}{{\Pr\left( {{ab}(p)} \right)} = {\sum\limits_{h \in \; H_{p}}{\Pr(h)}}} & (4)\end{matrix}$

To find a plan which achieves production goals while also beinginformative, the planner 30 evaluates the plans 54 in terms of theprobability T and uses this and the current plant state 58 topreferentially construct a plan 54 that achieves a production goal whilehaving a positive probability of failure. While in the short term thismay likely lower the productivity of the system 20, the informationgained allows improvement in long term productivity. The planner 30,moreover, may construct a sequence of plans 54 for execution in theplant 20 which might not be maximally informative individually, but aremaximally informative taken jointly.

As noted above, any form of search may be employed in the planner 30that piece-wise selects/generates from suitable plans that will achievea given production goal while yielding useful diagnostic informationwithin the scope of the present disclosure. A simple brute force searchcould be employed to generate all possible action sequences and theresulting list could be filtered to yield plans 54 that achieveproduction goals while being informative, as per the following equation(5):p ^(opt)=argmin_(achievesGoal(p)∈P) |Pr(ab(p))−T|  (5)

However, this may be impractical in real-time control applications ifthe space of plans P is very large. Another possible approach employedin the exemplary system 2 is for the diagnosis engine 40 to establish aheuristic by which the planner 30 considers sets or families of plans 54that share structure, such as by employing an A* target search using aset of partial plans p_(I→S) ₁ , p_(I→S) ₂ , . . . , p_(I→S) _(n) whichprogress from an initial state I to intermediate states S₁, S₂, . . . ,S_(n). In this approach, for each step, the planner 30 uses the A*target search to attempt to expand the plan most likely to achieve theproduction goal in the best (e.g., most informative) way. An ideal planp in this regard would start with the prefix p_(I→S) _(n) which takesthe system 20 to a state S_(n) and continues with the suffix plan p_(S)_(n) _(→G) leading from the state S_(n) to the goal state G. This A*technique chooses the partial plan p_(I→S) _(n) to expand using aheuristic function f(S_(n)) provided by the diagnosis engine 40 whichestimates the total path quality as the quality of the plan prefixp_(I→S) _(n) (written as g(S_(n))), plus the predicted quality of thesuffix p_(S) _(n) _(→G), (written as h(S_(n))), per the followingequation (6):f(S _(n))=g(S _(n))+h(S _(n)).  (6)

If the heuristic function f(S_(n)) never overestimates the true qualityof the complete the plan, then the heuristic f(S_(n)) is said to beadmissible and an A* target search by the planner 30 should return anoptimal plan 54. In this regard, the underestimation causes the A*search approach to be optimistic in the face of uncertainty, therebyensuring that uncertain plans are explored before committing tocompleted plans known to be high in quality. As a result, the moreaccurate the heuristic function is, the more the A* target searchfocuses on the highly informative plans 54. In the illustratedembodiments, therefore, the planner 30 employs a heuristic functionderived by the diagnosis engine 40 based at least partially on thedescription of the system architecture and dynamics in the plant model50.

FIG. 7 shows an exemplary state/action diagram 400 depicting possibleplans for transitioning the system state from a starting state S to agoal state G in the plant 20. In this example, the system state nodes402 include the starting state S 402 s, the goal stage G 402 g, and fourintermediate states 402 a-402 d for nodes A-D, respectively. A givenplan 54 for this example proceeds by following actions 404 through thediagram 400 to ultimately reach the goal G 402 g. One possible plan 54that satisfies such a production goal moves the system through the statesequence [S, A, C, G] through actions 404 sa, 404 ac, and 404 cg asshown in FIG. 7. Assuming for illustrative purposes that this plan 54results in an abnormal outcome caused by a faulty action 404 ac betweennodes A and C (action a_(A,C)), caused by a single persistent fault inone of the system resources 21-24, the diagnosis engine 40 woulddetermine from the plan 54 and the resulting fault observation 56 thatall of the actions 404 sa, 404 ac, and 404 cg along the plan path are(without further information) suspected of being faulty. Since a singlepersistent fault is assumed, there are three positive probabilityhypotheses corresponding to the suspected actions {{a_(S,A)},{a_(A,C}, {a) _(C,G)}}. Absent additional information, the diagnosisengine 40 initially assigns equal probabilities {⅓}, {⅓}, {⅓} to thesesuspected actions.

The diagnosis engine 40 uses the graph structure and probabilityestimates to construct heuristic bounds on the uncertainty that can becontributed to a plan by any plan suffix, in this example, by buildingup the heuristic from right to left in FIG. 7. In particular, theexemplary diagnosis engine 40 assigns lower and upper bounds [L,U] tothe nodes 402, as shown in FIG. 7, and these bound values are sent tothe planner 30 in one implementation. As an illustrative example, theaction a_(D,G) leading from state D to the goal state G in FIG. 3 wasnot part of the observed plan 54 that failed, and is therefore not acandidate hypothesis, and this action has a zero probability of beingthe source of the assumed single persistent system fault. Consequently,extending any prefix plan 54 ending in state D with action a_(D,G) willnot increase the failure probability of the extended plan 54, becausethe action a_(D,G) has probability zero of being abnormal. In thisexample, moreover, there are no other possible plans 54 from D to G, soboth the upper and lower bound for any plan ending in state D is zero,and the node D is thus labeled [0,0] in FIG. 7. State B 402 b likewisehas a lower bound of zero as plans 54 passing through state B can becompleted by an action a_(B,D) 404 bd that does not use a suspectedaction 404 and ends in state D which has a zero lower bound. State B inthis example has an upper bound of ⅓ since it can be completed by anunsuspected action a_(B,C) 404 bc to state C 402 c which in turn hasboth upper and lower bounds with ⅓ probability of being abnormal. Thediagnosis engine 40 continues this analysis recursively to determinebounds on the probability of a suffix sub-plan being abnormal, and sendsthese as part of the information gain data 70 to the planner 30.

The planner 30 uses these bounds with a forward A* target search toidentify and construct a plan 54 that achieves or most closelyapproximates the target probability T. For example, one possible plan 54begins from the start node S 402 s and includes a first action a_(S,A),which was part of the plan 54 that was observed to be abnormal. If theaction a_(S,A) 404 ac is added to a partial plan, it must add ⅓probability to the chance of failure as it is a candidate itself. Aftera_(S,A), the system 20 would be in state A, and a plan 54 could becompleted through D by including actions 404 ad and 404 dg to arrive atthe goal state G 402 g. The action a_(A,D) itself has a zero probabilityof being abnormal since it was not involved in the previously observedfaulty plan. Using the heuristic bound, therefore, a completion throughstate node D 402 d adds zero probability of being abnormal. From node A402 a, a plan 54 could alternatively be completed through node C, as inthe originally observed plan 54. The corresponding action a_(A,C) 404 acadds ⅓ probability of failure to such a plan and based on the heuristicbound the completion through C 402 c must add another ⅓ probability ofbeing abnormal.

The heuristic that is precomputed and provided by the diagnosis engine40 therefore allows prediction of total plan abnormality probability fora possible plan 54 that moves the system 20 through the state nodesequence [S, A, C, G] or [S, A, D, G]. The lower bound of the total planis ⅓, as determined by ⅓ from a_(S,A) plus 0 from the completiona_(A,D),a_(D,G), and the upper bound is 3/3 equal to the sum of ⅓ froma_(S,A) plus ⅓ each from a_(A,C) and a_(C,G). If this plan is computedthrough [a_(A,C),a_(C,G)] the total plan 54 will fail with probability1, and therefore nothing is to be learned from constructing such a plancompletion. If the plan 54 is instead completed through the suffix[a_(A,D),a_(D,G)] the failure probability of the total plan will be ⅓which is closer to the optimally informative probability T=0.5. In thiscase, the planner 30 will construct the plan 54 [S, A, D, G] forexecution in the plant 20. The plan 54 may or may not succeed, and ineither case something may be learned from a diagnostic perspective. Forinstance, if the plan [S, A, D, G] fails, the diagnosis engine 40 learnsthat node a_(S,A) was the failed action (for the assumed singlepersistent fault scenario), and if the plan 54 is successful, the engine40 can further refine the belief model 42 by eliminating action 404 saas a fault suspect.

It is noted that there is no guarantee that a plan 54 exists for anygiven value between the bounds. The diagnosis engine 40 recursivelycalculates the heuristic bounds starting from all goal states, where agoal state has an empty set of suffix plans p_(G→G)=ø and therefore hasa set lower bound L_(G)=0 and a set upper bound U_(G)=0. For each newstate S_(m), the diagnosis engine 40 calculates the corresponding boundsbased at least partially on the bounds of all possible successor statesSUC(S_(m)) and the failure probability of the connecting actiona_(Sm,Sn) between S_(m) and a successor state S_(n). In this regard, asuccessor state S_(n) of a state S_(m) is any state that can be reachedin a single step starting from the state S_(m). In the case where asingle fault is assumed, the failure probability added to a plan p_(I→S)_(m) by concatenating an action a_(S) _(m) _(,S) _(n) , is independentfrom the plan p_(I→S) _(m) if

∩

=ø. The diagnosis engine 40 determines the lower bound for S_(m) by theaction probabilities linking S_(m) to its immediate successors and thelower bounds on these successors, and the diagnosis engine 40 computesthe upper bounds in analogous fashion withL_(Sm)=min_(Sn∈SUC(Sm))[Pr(ab(a_(Sm,Sn)))+L_(Sn)], andU_(Sm)=max_(Sn∈SUC(Sm))[Pr(ab(a_(Sm,Sn)))+U_(Sn)].

In contrast to the computation of the heuristic in the diagnosis engine40, the search for an informative production plan by the planner 30starts from the initial starting state S 402 a and works recursivelyforward toward the goal state 402 g. The abnormality probability of theempty plan starting at the initial state S is zero plus the bestcompletion. In general, the planner 30 computes the abnormalityprobability as the plan probability up to the current state plus theabnormality probability of the best completion route. Since the planner30 is initially uncertain about the completion, its probability ofabnormality is an interval that includes a lower and upper bound and thevalues in between. As a result, the total abnormality probability isalso an interval, as set forth in the following equation (7):I(p _(I→Sn))=[Pr(ab(p _(I→Sn)))+L _(Sn) ,Pr(ab(p _(I→Sn)))+U_(Sn))]  (7)

As noted above, the most informative plan 54 is one whose total failureprobability is T, with T=0.5 in a preferred implementation for anassumed persistent single fault. Given an interval describing bounds onthe total abnormality probability of a plan I(p_(I→S) _(n) ), theplanner 30 can therefore construct an interval describing how close theabnormality probabilities will be to T according to the followingequation (8):|T−I(p _(I→S) _(n) )|  (8)

This absolute value in equation (8) folds the range around T, and if theestimated total abnormality probability of the plan 54 straddles targetprobability T, then the interval |T−I(p_(I→S) _(n) )| straddles zero andthe interval will range from zero to the absolute max of I(p_(I→S) _(n)). The exemplary planner 30 uses a search heuristic F(p_(I→S) _(n))=min(|T−I(p_(I→S) _(n) )|) provided by the diagnosis engine 40 as partof the expected information gain data 70, although other heuristics arecontemplated within the scope of the disclosure which allow targetsearching to construct plans 54 having high relative informative value.The exemplary function F has some advantageous properties. For example,whenever the predicted total plan abnormality probability lies between Land U, F is zero. Also, plans 54 may exist whose abnormality probabilityexactly achieves the target probability T. Moreover, in all casesF(p_(I→S) _(n) ) represents the closest any plan that goes through astate S_(n) can come to the target abnormality probability exactly T.

The planner 30 can search from a whole set of partial plans P={p_(I→S) ₁, p_(I→S) ₂ , . . . , p_(I→S) _(n) } (e.g., stored in the planner 30,the data store 36, or elsewhere in the system 2 or in an external datastore accessible by the planner 30). For each partial plan, the planner30 evaluates F(p_(I→S) _(n) ) and expands the plan with the lowestvalue. Since F(p_(I→) _(n) ) is an underestimate, an A* search usingthis estimate will return the most informative plan that achievesproduction goals.

In a further aspect of the disclosure, the planner 30 may be operativeto improve the efficiency of the target plan search using selectivepruning. In this regard, the above described search heuristic in manycases may return the same value, i.e., zero, which provides the planner30 with little guidance in making a selection. The planner 30 mayaccordingly be adapted to focus the search using one or more techniques.In a first focusing approach, the planner 30 prunes out dominated partsof the search space. For example, a given partial plan I(p_(I→S) _(n) )may be identified by the planner 30 having an abnormality probabilityinterval that does not straddle the target value T. The best possibleplan in this interval will be on the one of the two boundaries of theinterval that is closest to the target value T. For instance, letL_(I)(p_(I→S) _(n) ) and U_(I)(p_(I→S) _(n) ) be the lower and upperbound of the abnormality probability interval I(p_(I→S) _(n) ). Theplanner 30 determines the value of the best plan V_(p) _(I→Sn) in suchcases according to the following equation (9):V _(pI→S) _(n) =min(|L _(I(pI→S) _(n) ₎ −T|,|U _(I(pI→S) _(n) ₎−T|)  (9)

The plan p_(I→S) _(i) will dominate every plan p_(I→S) _(j) where

<

T∉I(p_(I→S)). The planner 30 accordingly operates to prune out(eliminate from further consideration) some or preferably all dominatedplans from the A* search space.

In another aspect of the disclosure, the planner 30 may employ otherfocusing techniques to intelligently break ties in the heuristic value.As noted above, the heuristic value determines which state node will beexpanded next, but it is possible that two or more nodes will receivethe same heuristic value. Accordingly, the planner 30 may employ one ormore rules to break the tie and hence to determine which node should beexpanded first. One suitable rule in this regard is to simply pick anode randomly.

A further improvement can be implemented in the planner 30 according tothis aspect of the disclosure, using the fact that V_(pI→S) _(n) (inequation (9) above) represents a guaranteed lower bound on a total planP_(I→G) starting with the partial plan p_(I→S) _(n) as prefix. While theupper and lower bounds are realizable, none of the interior points ofthe interval are guaranteed to exist. Therefore, the planner 30 mayadvantageously compare the V's in order to decide which of two partialplans has the closest realizable solution to break the above mentionedties. Moreover, if two partial plans are also identical in thisparameter, the information gain is the same, and thus the planner 30 isoperative to choose the partial plan that has less likelihood to fail,thereby facilitating short term productivity. The planner 30 is thisembodiment may combine these two approaches in a sequential decisionprocedure. For example, if p_(I→S) ₁ and p_(I→S) ₂ are two partial planswith the same minimum value, i.e. F(p_(I→S) ₁ )=F(p_(I→S) ₂ ), theplanner 30 will break the tie by choosing the first rule that appliesfrom the following ordered list:

1 If

<

then expand p_(I→S) ₁ first;

2 If

>

then expand p_(I→S) ₂ first;

3 If U_(I)(p_(I→S) ₁ )<U_(I)(p_(I→S) ₂ ) then expand p_(I→S) ₁ first;

4 If U_(I)(p_(I→S) ₁ )>U_(I)(p_(I→S) ₂ ) then expand p_(I→S) ₂ first;

5 If L_(I)(p_(I→S) ₁ )<L_(I)(p_(I→S) ₂ ) then expand p_(I→S) ₂ first;

6 If L_(I)(p_(I→S) ₁ )>L_(I)(p_(I→S) ₂ ) then expand p_(I→S) ₁ first;

7 otherwise pick randomly.

The planner 30 can also facilitate the selective avoidance of knownfaulty resources 21-24 in the plant 20 via the component 32 b, as wellas generation of plans 54 so as to help determine the source of faultsobserved during production. For example, the planner 30 operating theabove described modular printing system plant 20 of FIG. 2 can beinfluenced by diagnostic objectives 34 b (FIG. 3) to preferentiallyconstruct paper paths via appropriate routing of substrates to usedifferent subsets of routing and printing components 24 and 22, where agiven sequence of these paths can be used to isolate the cause of anobserved fault. Moreover, multiple plant pathways, redundancy of plantresources, and the capability to operate resources at different speeds,voltage levels, temperatures, or other flexibility in settingoperational parameters of the plant resources allows the planner 30 totailor active production plan generation for intelligent diagnosticinformation gain despite lack of complete sensor coverage in a givenplant 20. In this manner, the modularity and flexibility of a givensystem 20 can be exploited by the pervasive diagnostic features of thecontrol system 2 to facilitate diagnostic objectives 34 b while alsoproviding benefits with regard to flexibility in achieving productiongoals.

The control system 2 can thus provide the advantages of performingdiagnosis functions during production, even with limited sensorcapabilities, with the flexibility to schedule dedicated diagnosticplans 54 if/when needed or highly informative. In the case of explicitdedicated diagnosis, the planner 30 focuses on the needs of thediagnosis engine 40 and thus creates/selects plans 54 that maximizeinformation gain with respect to the fault hypotheses. The system 2 alsoallows the generation of plans 54 solely on the basis of productiongoals, for instance, where there is only one plan 54 that can perform agiven production task and the planner 30 need not chose from a set ofequivalent plans, thereby limiting the information gathering to the caseof passive diagnosis for that plan.

In the exemplary modular printing system example 20 above, therefore,the control system 2 can choose to parallelize production to the extentpossible, use specialized print engines 22 for specific printing tasks,and have the operational control to reroute sheet substrates aroundfailed modules as these are identified. In this implementation, theplanner 30 may receive a production print job 51 from a job queue (inthe producer 10, or a queue in the planner 30), and one or more plans 54are constructed as described above to implement the job 51. Theobservations 56 are provided to the diagnosis engine 40 upon executionof the plan(s) 54 to indicate whether the plan 54 succeeded withoutfaults (e.g., not abnormal), or whether an abnormal fault was observed(e.g., bent corners and/or wrinkles detected by the sensors 26 inprinted substrates). The diagnosis engine 30 updates the hypothesisprobabilities of the belief model 42 based on the executed plan 54 andthe observations 56. When a fault occurs, the planner 30 constructs themost informative plan 54 in subsequent scheduling so as to satisfy thediagnostic objectives 34 b. In this regard, there may be a delay betweensubmitting a plan 54 to the plant 20 and receiving the observations 56,and the planner 30 may accordingly plan production jobs 51 from the jobqueue without optimizing for information gain until the outcome isreturned in order to maintain high short term productivity in the plant20.

Using the above described pervasive diagnosis, the plan construction inthe planner 30 is biased to have an outcome probability closest to thetarget T, and this bias can create paths capable of isolating faults inspecific actions. Prior to detection of a system fault, the plant 20 mayproduce products 52 at a nominal rate r_(nom), with diagnosis effortsbeginning once some abnormal outcome is observed. The length of timerequired to diagnose a given fault in the system (e.g., to identifyfaulty plant components or resources 21-24) will be short if dedicated,explicit diagnostic plans 54 are selected, with pervasive diagnosisapproaches taking somewhat longer, and passive diagnostic techniquestaking much longer and possibly not being able to completely diagnosethe problem(s). With regard to diagnosis cost, however, explicitdedicated diagnosis results in high production loss (production ishalted), while purely passive diagnosis incurs the highest expectedrepair costs due to its lower quality diagnosis. The pervasive diagnosisaspects of the present disclosure advantageously integrate diagnosticobjectives 34 b into production planning by operation of the planner 30,and therefore facilitate realization of a lower minimal total expectedproduction loss in comparison to passive and explicit diagnosis.

The passive diagnostic aspects of the disclosure, moreover, aregenerally applicable to a wide class of production manufacturingproblems in which it is important to optimize efficiency but the cost offailure for any one job is low compared to stopping the productionsystem to perform explicit diagnosis. In addition, the disclosure findsutility in association with non-manufacturing production systems, forexample, service industry organizations can employ the pervasivediagnostic techniques in systems that produce services using machines,software, and/or human resources. Moreover, the disclosure is notlimited to a probability based A* search, wherein other planconstruction techniques can be employed such as a SAT-solver approach inwhich the clauses represent failed plans and each satisfying assignmentis interpreted as a valid diagnosis.

Referring also to FIGS. 8-16, the above described heuristic search bythe planner 30 was simulated to evaluate the cost advantages ofpervasive diagnosis in a model of a modular digital printing press basedon the above described printing plant 20 in FIG. 2. In this modularsystem 20, multiple pathways allow parallel production, use ofspecialized print engines 22 for specific sheets, and selectivererouting around failed modules 21, 22, etc. In the simulation, theplanner 40 sends a plan 54 to a simulation of the printing system 20which models the physical dynamics of the paper moving through thesystem 20 and determines the outcome. If the plan 54 is completedwithout any faults (e.g., bent corners or wrinkles) and deposited in therequested finisher tray 23, the plan 54 is deemed to have succeeded (notabnormal), and otherwise the plan 54 outcome is determined to beabnormal. The original plan 54 and the observed outcome 56 are sent tothe diagnosis engine 40 which updates the hypothesis probabilities ofthe belief model 42.

In the simulation, a system module (e.g., one of the print engines 22)may exhibit faulty behavior with some probability q (also referred to asan intermittency rate), resulting in plan failure, where persistentfault resources 21-24 (e.g., modules that cause a fault every time theyare used) have an intermittency of 1. The simulation of costs employed asimple cost model of opportunity costs in terms of unrealized productiondue to efforts of isolating the faulty component (diagnosis costs) andexchanging this component (repair costs). The cost in this modelrepresents the expected total amount of lost production due to a fault.When a fault is first observed, the cost is 1 (lost unit of production)and the belief state 42 is a uniform distribution over all faulthypothesis for all approaches. With the passive diagnostic approach, theplant 20 continues production at the normal rate r_(nom), whereas fordedicated (explicit) diagnostics in the simulation, the plant 20produces products 52 at a reduced rate r_(perv)≦r_(diag) duringdiagnosis, and since faulty products can be produced, the cost iscalculated by the following equation 10:c _(diag) ^(t,per)=1+n _(faulty)+(r _(nom) −r _(perv))*t _(diag)  (10)

In the simulated results, the exchange time for replacing a singlemodule 22 was assumed to be 10 minutes, and this replacement causesshutdown of only one print engine 22 at the time. Since the exemplaryplant 20 employs four print engines 22, the simulated exchange time wasset as t_(exc)=150 sec. The simulation also employed a nominal printrate r_(nom)=3.1 sheets/sec, and the simulation showed a reduced rate ofpervasive diagnosis r_(perv)=1.9 sheets/sec. Moreover, the experimentalresults were averaged over 100 runs to reduce statistical variation.Table 1 below summarizes the simulated results for three differentintermittency rates q=0.01, 0.20, and 1.00, respectively, in which thepervasive diagnostics described above results in the lowest rate of lostproduction (e.g., number of exchanged modules 22, the number ofexchanged modules at the minimal response cost).

TABLE 1 min. response cost Time # of exch. mod. q = 0.01 Passive 1010.22214.1 2.01 Explicit 947.25 76.6 1.41 Pervasive 768.80 204.6 1.01 q = 0.1Passive 1055.25 35.0 2.10 Explicit 591.31 29.1 1 Pervasive 547.77 37.2 1q = 1.0 Passive 1012.00 7.78 2.01 Explicit 515.43 3.1 1 Pervasive 509.763.78 1

FIGS. 8-10 illustrate cost vs. time graphs 510, 520, and 530 for thesimulation for the case of intermittency rate q=0.01. When q=0.01 afaulty action only causes the plan to fail with a statistical mean of1/100. The graph 510 in FIG. 8 shows instantaneous repair cost for thecases of passive diagnostics 511, explicit (dedicated) diagnostics 512and pervasive diagnostics 513. Cumulative diagnosis costs vs. time areshown in the graph 520 of FIG. 9, including curves 521, 522, and 523 forpassive, explicit, and pervasive diagnostic techniques. The graph 530 inFIG. 10 illustrates passive, explicit, and pervasive diagnostic costcurves 531, 532, and 533, respectively, for response cost (diagnosis andrepair) vs. time. For less intermittent faults (q=0.10), FIGS. 11-13depict instantaneous repair cost, cumulative diagnosis cost, andresponse cost graphs 610, 620, and 630, respectively, as a function oftime. The graph 610 in FIG. 11 illustrates passive, explicit, andpervasive cost curves 611, 612, and 613, respectively, for instantaneousrepair cost. In FIG. 12, cumulative diagnosis cost curves 621, 622, and623 are shown for passive, explicit, and pervasive diagnostictechniques, and the graph 630 in FIG. 13 shows passive, explicit, andpervasive cost curves 631, 632, and 633 for repair costs vs. time. FIGS.14-16 provide cost vs. time graphs 710, 720, and 720 for instantaneousrepair costs, cumulative diagnostic cost, and response cost,respectively, for the case of persistent faults (q=1.00). Graph 710 inFIG. 14 shows passive, explicit, and pervasive instantaneous repair costcurves 711, 712, and 713, respectively. For cumulative diagnosis costsat q=1.00, FIG. 15 shows curves 722, 723, and 723 for passive, explicit,and pervasive diagnosis, respectively. In FIG. 16, the graph 730 showspassive, explicit, and pervasive diagnosis response cost curves 731,732, and 733, respectively.

The instantaneous repair costs in FIGS. 8, 11, and 14 was computed byestimating the repair time based on the current probability distributionover the fault hypothesis and pricing this downtime according to thenominal machine production rate. The diagnosis cost in FIGS. 9, 12, and15 at a given time t was calculated as the accumulated productiondeficit in relation to a healthy machine producing at its nominal rater_(nom), where the x-axis is the amount of time (relative to the firstoccurrence of the fault) after which one chooses to stop diagnosis andstart repairing the machine. The minimum of the sum these costs denotesthe optimal point in time (relative to first occurrence of the fault) toswitch from diagnosis to repair and gives the minimal expected totalloss of production due to the fault.

In the simulations, the optimal response cost of pervasive diagnosis isbelow those of the other two approaches, and the shortest diagnosisduration is for explicit, with pervasive and passive diagnosistechniques taking successively longer. However, the explicit diagnosticapproach involves the highest production loss since production is haltedduring diagnosis, whereby explicit diagnosis does not result in minimalresponse costs. Passive diagnosis has the lowest rate of lostproduction, but incurs the highest expected repair costs due to itslower quality diagnosis, due to plans 54 being constructed and executedsolely on the basis of production goals and objectives 34 a irrespectiveof diagnostic objectives 34 b. Pervasive diagnosis, on the other hand,intelligently integrates the diagnostic objectives 34 b into productionplanning by using the flexibility of the planner 30 and the diagnosisengine 40, and the simulated results show a lower minimal total expectedproduction loss in comparison to passive and explicit diagnosisapproaches.

Referring now to FIGS. 3 and 17, the planner 30 may employ a BooleanSatisfiability problem (SAT) solver 38 (FIG. 3) in selecting plans 54for execution in the plant 20 using the guidance of the diagnosis engine40. In this implementation, the pervasive diagnosis tasks are translatedinto logical encodings (e.g., CNF, DNNF, BDD, PI, HTMS) to include allpossible bounded length plans, and the encoding can be solved in theplanner 30 using a SAT solver 38 to answer diagnosis queries such asfinding a plan that uses a certain set of modules 22 in the plant 20.This technique allows the planner to submit queries to the SAT solver 38instead of having to search for the plans 54 via A* heuristic search orsimple brute force search techniques as described above.

FIG. 17 illustrates this approach in a diagram 800. As shown in FIG. 17,the process begins with a CNF formulation that encapsulates all possibleplans with fixed bound on (i.e., a sequence of bounded length executableactions by a given system). Additional variables corresponding tomodules are included in the encoding. Additional formulas are includedto ensure that a module variable is TRUE only if some action that usesthat module is executed. At 802 in FIG. 17, the plan constructioncomponent 32 formulates the plan generation problem based on theproduction goals and diagnostic objectives 34 b, and uses the currentplant condition 58 from the diagnosis engine 40 to derive a list ofsuspected actions and/or plant modules 22 at 812. These are provided toa translation component 804 in the planner 30 that generates a SATformulation 814.

The SAT problem formulation 814 is then provided to a SAT solver 38,such as by a query to the solver component 38 in FIG. 3, and the solver38 generates a SAT solution 816. The solution 816 is then translated at808 to yield a generated plan 54 at 818 for execution in the plant 20.As a diagnostic objective 34 b may be to reduce the set of suspectmodules 22 in the plant 20, the solver 38 generates a set of modules 22that should be used in the next plan execution, for which a set ofmodules can be identified by the solver 38 using a maximizing entropyheuristic. In this case, the plan construction component 32 queries theSAT solver 38 to construct a set of modules 22 having close to 0.5probability of failure. Once the generated plan 54 is identified by thesolver 38, it is provided to the plant 20 by the planner 30 andexecuted. The plan 54 and the corresponding observations 56 are providedto the diagnosis engine 40 which updates the current condition 58 andthe belief model 42 to reduce the set of suspected modules 22, and thediagnosis engine 40 or the planner 30 add appropriate formulas to theSAT encoding to reflect those changes. This process is continued in oneimplementation until the set of suspected modules cannot be reduced.

Compared to the heuristic A* search approach above, the SAT solverapproach in FIG. 17 is not as easily scaled up for large complex systems20, but is adaptable to simple modular systems, and may advantageouslyemploy off-the shelf SAT solvers to solve the plan generation problem inthe planner 30. Moreover, the SAT solver approach captures all plans 54,and a wide range of queries can be posted to the SAT solver 38 by theplan construction component 32 in generating a plan to accommodatediagnostic objectives 34 b. Moreover, the SAT problem can be formulatedin any suitable encoding, including without limitation ConstraintSatisfaction (CSP) and Integer Linear Programming (ILP).

The above examples are merely illustrative of several possibleembodiments of the present disclosure, wherein equivalent alterationsand/or modifications will occur to others skilled in the art uponreading and understanding this specification and the annexed drawings.In particular regard to the various functions performed by the abovedescribed components (assemblies, devices, systems, circuits, and thelike), the terms (including a reference to a “means”) used to describesuch components are intended to correspond, unless otherwise indicated,to any component, such as hardware, software, or combinations thereof,which performs the specified function of the described component (i.e.,that is functionally equivalent), even though not structurallyequivalent to the disclosed structure which performs the function in theillustrated implementations of the disclosure. In addition, although aparticular feature of the disclosure may have been disclosed withrespect to only one of several embodiments, such feature may be combinedwith one or more other features of the other implementations as may bedesired and advantageous for any given or particular application. Also,to the extent that the terms “including”, “includes”, “having”, “has”,“with”, or variants thereof are used in the detailed description and/orin the claims, such terms are intended to be inclusive in a mannersimilar to the term “comprising”. It will be appreciated that various ofthe above-disclosed and other features and functions, or alternativesthereof, may be desirably combined into many other different systems orapplications, and further that various presently unforeseen orunanticipated alternatives, modifications, variations or improvementstherein may be subsequently made by those skilled in the art which arealso intended to be encompassed by the following claims.

1. A production control system for controlling operation of a productionsystem with a plant that can achieve one or more production goals, thecontrol system comprising: a planner operatively coupled with theproduction system to provide one or more plans for execution in theplant based on at least one production goal; a plant model operativelycoupled with the planner and including a model of the plant; and adiagnosis engine operatively coupled with the planner, the productionsystem, and the model, the diagnosis engine operative to determine acurrent plant condition based at least partially on a previouslyexecuted plan, at least one corresponding observation from the plant,and the plant model, and to determine expected information gain datarepresenting diagnostic value for one or more possible plans or partialplans based on the current plant condition and the model; wherein theplanner is operative to construct or select at least one production planfor the plant that concurrently achieves at least one production goaland at least one diagnostic objective relating to identifying resourcescausing intermittent or persistent faults based at least partially onthe current plant condition, the plant model, and the expectedinformation gain data from the diagnosis engine.
 2. The control systemof claim 1, wherein the planner is operative to selectively provide adedicated diagnostic plan for execution in the plant at least partiallybased on at least one diagnostic objective and the current plantcondition.
 3. The control system of claim 2, further comprising anoperator interface operatively coupled with the diagnosis engine toallow an operator to define a diagnostic job using a diagnosis jobdescription language.
 4. The control system of claim 2, wherein theplanner is operative to selectively provide interleaved dedicateddiagnostic plans and production plans for execution in the plant atleast partially based on at least one production objective and at leastone diagnostic objective.
 5. The control system of claim 4, wherein theplanner is operative to use the current plant condition in providing theinterleaved dedicated diagnostic plans and production plans forexecution in the plant.
 6. The control system of claim 1, wherein thediagnosis engine formulates a heuristic associated with the planconstruction, and wherein the planner employs a partial-plan searchusing the heuristic to construct the plans for execution in the plant.7. The control system of claim 1, further comprising a plan data storeincluding a plurality of whole or partial plans selectable by theplanner for execution in the plant to facilitate one or more productionor diagnostic objectives.
 8. The control system of claim 1, furthercomprising an operator interface operatively coupled with the diagnosisengine to provide operator observations to the diagnosis engine, whereinthe diagnosis engine is operative to determine the current plantcondition based at least partially on the operator observations.
 9. Thecontrol system of claim 1, wherein the planner is operative to use thecurrent plant condition in making a tradeoff between productionobjectives and diagnostic objectives in constructing or selecting plansfor execution in the plant.
 10. The control system of claim 1, whereinthe planner is operative to use the current plant condition inconstructing or selecting plans for execution to perform diagnosis inisolating faulty resources in the plant.
 11. The control system of claim1, wherein the planner is operative to use the current plant conditionin constructing or selecting plans for execution to perform prognosisabout a remaining useful life of plant components or resources.
 12. Amethod of generating plans for execution in a production system with aplant to achieve one or more production goals, the method comprising:determining a current plant condition based at least partially on apreviously executed plan, at least one corresponding observation fromthe plant, and a plant model; determining expected information gain datarepresenting diagnostic value for a plurality of possible plans orpartial plans based on the current plant condition and the model; andusing a processor, constructing or selecting a production plan that willconcurrently achieve a given production goal and a diagnostic objectiverelating to identifying resources causing intermittent or persistentfaults based at least partially on the current plant condition and theexpected information gain data.
 13. The method of claim 12, whereinconstructing or selecting the plan includes making a tradeoff betweenproduction objectives and diagnostic objectives based at least partiallyon the current plant condition.
 14. The method of claim 12, whereinconstructing or selecting the plan includes performing diagnosis toisolate faulty resources in the plant based at least partially on thecurrent plant condition.
 15. The method of claim 12, further comprisingconstructing or selecting a dedicated diagnostic plan for execution inthe plant based at least partially on at least one diagnostic objectiveand the current plant condition.
 16. The method of claim 15, furthercomprising selectively interleaving dedicated diagnostic plans andproduction plans based on at least one production objective and at leastone diagnostic objective.
 17. The method of claim 15, further comprisingallowing an operator to define a diagnostic plan using a diagnosis jobdescription language.
 18. The method of claim 12, further comprisingreceiving operator observations, wherein constructing or selecting theplan is based at least partially on the operator observations.
 19. Anon-transitory computer readable medium having computer executableinstructions for performing the steps of: determining a current plantcondition in a production system plant based at least partially on apreviously executed plan, at least one corresponding observation fromthe plant, and a plant model; determining expected information gain datarepresenting diagnostic value for a plurality of possible plans orpartial plans based on the current plant condition and the model; andconstructing or selecting a production plan that will concurrentlyachieve a given production goal and a diagnostic objective relating toidentifying resources causing intermittent or persistent faults based atleast partially on the current plant condition and the expectedinformation gain data.